New Theorems for Oscillations to Differential Equations with Mixed Delays

Santra, Shyam Sundar; Majumder, Debasish; Bhattacharjee, Rupak; Bazighifan, Omar; Khedher, Khaled Mohamed; Marin, Marin

doi:10.3390/sym13030367

Open AccessArticle

New Theorems for Oscillations to Differential Equations with Mixed Delays

by

Shyam Sundar Santra

^1,*,†

,

Debasish Majumder

^1,†,

Rupak Bhattacharjee

^1,†,

Omar Bazighifan

^2,*,†

,

Khaled Mohamed Khedher

^3,4,†

and

Marin Marin

^5,*,†

¹

Department of Mathematics, JIS College of Engineering, Kalyani 741235, India

²

Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen

³

Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia

⁴

Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia

⁵

Department of Mathematics and Computers Science, Transilvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania

^*

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Symmetry 2021, 13(3), 367; https://doi.org/10.3390/sym13030367

Submission received: 8 February 2021 / Revised: 19 February 2021 / Accepted: 23 February 2021 / Published: 25 February 2021

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications)

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Abstract

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form

{(p (ι) {(w^{'} (ι))}^{α})}^{'} + r (ι) u^{β} (ν (ι)) = 0, ι \geq ι_{0}

where

w (ι) = u (ι) + q (ι) u (ζ (ι)) .

Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Keywords: Lebesgue’s dominated convergence theorem; neutral; oscillation; nonoscillation; non-linear

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MDPI and ACS Style

Santra, S.S.; Majumder, D.; Bhattacharjee, R.; Bazighifan, O.; Khedher, K.M.; Marin, M. New Theorems for Oscillations to Differential Equations with Mixed Delays. Symmetry 2021, 13, 367. https://doi.org/10.3390/sym13030367

AMA Style

Santra SS, Majumder D, Bhattacharjee R, Bazighifan O, Khedher KM, Marin M. New Theorems for Oscillations to Differential Equations with Mixed Delays. Symmetry. 2021; 13(3):367. https://doi.org/10.3390/sym13030367

Chicago/Turabian Style

Santra, Shyam Sundar, Debasish Majumder, Rupak Bhattacharjee, Omar Bazighifan, Khaled Mohamed Khedher, and Marin Marin. 2021. "New Theorems for Oscillations to Differential Equations with Mixed Delays" Symmetry 13, no. 3: 367. https://doi.org/10.3390/sym13030367

APA Style

Santra, S. S., Majumder, D., Bhattacharjee, R., Bazighifan, O., Khedher, K. M., & Marin, M. (2021). New Theorems for Oscillations to Differential Equations with Mixed Delays. Symmetry, 13(3), 367. https://doi.org/10.3390/sym13030367

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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